Problem: The base of a triangle is 80, and one of the base angles is 60∘. The sum of the other two sides is 90. The shortest side of the triangle is:
Answer Choices:
A. 45
B. 40
C. 36
D. 17
E. 12
Solution:
Let the triangle be ABC, with AB=80, BC=a, CA=b=90−a, and ∠B=60∘. Let CD be the altitude to AB. Let x=BD.